Lifted Tree-Reweighted Variational Inference

Hung Bui Nuance, Tuyen Huynh Jon von Neumann Institute Vietnam National University Ho Chi Minh City, David Sontag New York University
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:391-400, 2014.

Abstract

We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the treereweighted variational objective lends itself to a compact lifted formulation which can be solved much more efficiently than the standard TRW formulation for the ground graphical model. Compared to earlier work on lifted belief propagation, our formulation leads to a convex optimization problem for lifted marginal inference and provides an upper bound on the partition function. We provide two approaches for improving the lifted TRW upper bound. The first is a method for efficiently computing maximum spanning trees in highly symmetric graphs, which can be used to optimize the TRW edge appearance probabilities. The second is a method for tightening the relaxation of the marginal polytope using lifted cycle inequalities and novel exchangeable cluster consistency constraints.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-nuance14a, title = {Lifted Tree-Reweighted Variational Inference}, author = {Nuance, Hung Bui and City, Tuyen Huynh Jon von Neumann Institute Vietnam National University Ho Chi Minh and University, David Sontag New York}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {391--400}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/nuance14a/nuance14a.pdf}, url = {https://proceedings.mlr.press/r12/nuance14a.html}, abstract = {We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the treereweighted variational objective lends itself to a compact lifted formulation which can be solved much more efficiently than the standard TRW formulation for the ground graphical model. Compared to earlier work on lifted belief propagation, our formulation leads to a convex optimization problem for lifted marginal inference and provides an upper bound on the partition function. We provide two approaches for improving the lifted TRW upper bound. The first is a method for efficiently computing maximum spanning trees in highly symmetric graphs, which can be used to optimize the TRW edge appearance probabilities. The second is a method for tightening the relaxation of the marginal polytope using lifted cycle inequalities and novel exchangeable cluster consistency constraints.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Lifted Tree-Reweighted Variational Inference %A Hung Bui Nuance %A Tuyen Huynh Jon von Neumann Institute Vietnam National University Ho Chi Minh City %A David Sontag New York University %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-nuance14a %I PMLR %P 391--400 %U https://proceedings.mlr.press/r12/nuance14a.html %V R12 %X We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the treereweighted variational objective lends itself to a compact lifted formulation which can be solved much more efficiently than the standard TRW formulation for the ground graphical model. Compared to earlier work on lifted belief propagation, our formulation leads to a convex optimization problem for lifted marginal inference and provides an upper bound on the partition function. We provide two approaches for improving the lifted TRW upper bound. The first is a method for efficiently computing maximum spanning trees in highly symmetric graphs, which can be used to optimize the TRW edge appearance probabilities. The second is a method for tightening the relaxation of the marginal polytope using lifted cycle inequalities and novel exchangeable cluster consistency constraints. %Z Reissued by PMLR on 04 October 2026.
APA
Nuance, H.B., City, T.H.J.v.N.I.V.N.U.H.C.M. & University, D.S.N.Y.. (2014). Lifted Tree-Reweighted Variational Inference. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:391-400 Available from https://proceedings.mlr.press/r12/nuance14a.html. Reissued by PMLR on 04 October 2026.

Related Material